1099 Software: Other than the presentation of the number on the actual form mailed out, does the hyphenation of the TIN number matter when filing?

Yes.  The TIN and TIN TYPE are efiled to the IRS.  If the TIN has 1-hyphen or dash, then its an EIN and that TIN TYPE is transmitted along with the TIN.  If the TIN has 2-hyphens, then the TYPE is SSN.  And if the TIN has no hyphens, the TIN TYPE is unknown.